Experimental demonstration of robust quantum steering

Quantum communication protocols have come a long way from abstract theoretical models to everyday
technological applications. Such protocols demonstrate quantum advantage compared to their classical
counterparts by utilizing non-classical resources such as coherence, entanglement, and measurement
incompatibility.
Their verification is typically performed in a device-dependent manner, which implies the underlying assumption that the measurement devices in the laboratory perform precisely as their manufacturer promises. However, there is no guarantee that these will function exactly as expected and will not be exploited by an adversary. Moreover, making such assumptions is very resource expensive. Hence, one would like to preferably use a completely trust free protocol such as a Bell test [1,2]. However, the realization of such tests is experimentally challenging and extremely resource intensive, despite today's technology.
Quantum steering protocols provide an alternative to Bell tests which is robust to experimental imperfections and noise [3-7]. These semi-device independent tasks require to trust only one party's measurement devices while the other party's devices are treated as black boxes. To bring quantum steering closer to the desired Bell tests we investigated to promising classed of steering criteria -- generalised entropic steering criteria based on Shannon, Tsallis, and Renyi entropies [8-10] and dimension-bounded steering inequalities [11].
Entropic steering criteria allow for detection of a large class of two-qubit states, can be extended to high dimensional systems, and have been reported to have a detection advantage over linear steering inequalities in terms of noise robustness [8]. Whilst dimension-bounded steering inequalities allow for demonstration of steering with minimal trust by simplifying Bob's devices to the number of degrees of freedom they are monitoring. Further, we investigate the robustness to measurement-reference-frames to test for applicability in near-term quantum applications such as quantum fibre networks [12].
In this talk I will discuss how we experimentally tested these steering protocols for a shared photonic two-qubit state with two and three measurement settings per side [13]. Our results show that entropy-based criteria are robust against imperfections in state preparation, however, there is an advantage in dimension-bounded steering in the presence of measurement imprecision. Further, we show that dimension-bounded steering is robust even in the case maximal misalignment of measurement settings between the parties and for the case of non-orthogonal measurement settings. We conclude with an analysis of the probability of violating the steering inequality and find that we reach 100% probability [12].
This noise robust demonstration of steering with minimal assumptions brings quantum steering protocols much closer to Bell tests without the sacrifice of extremely high-end equipment and has strong potential for applications in quantum fibre networks.

References
[1] J. Bell, Phys. 1, 195 (1964).
[2] N. Brunner et al., Rev. Mod. Phys. 86, 419 (2014).
[3] H. M. Wiseman et al., Phys. Rev. Lett. 98, 140402 (2007).
[4] D. Cavalcanti, and P. Skrzypczyk, Rep. Prog. Phys. 80, 024001 (2017).
[5] R. Uola et al., Rev. Mod. Phys. 92.1: 015001 (2020).
[6] M. M. Weston et al., Sci. Adv. 4, e1701230 (2018).
[7] S. Wollmann et al., Phys. Rev. A 98, 022333 (2018).
[8] A. C. S. Costa et al., Phys. Rev. A 98, 050104(R) (2018).
[9] J. Schneeloch et al., Phys. Rev. A 87, 062103 (2013).
[10] T. Krivachy et al., Phys. Rev. A 98, 062111 (2018).
[11] T. Moroder et al., Phys. Rev Lett. 116.9, 090403 (2016).
[12] S.K. Joshi et al., Science Adv. 6.36: eaba0959 (2020).
[13] S. Wollmann, U. Roope, and A.C.S Costa, Phys. Rev. Lett. 125.2: 020404 (2020).